FOKKER-PLANCK AND LANDAU-LIFSHITZ-BLOCH EQUATIONS FOR CLASSICAL FERROMAGNETS

A macroscopic equation of motion for the magnetization of a ferromagne t at elevated temperatures should contain both transverse and longitud inal relaxation terms and interpolate between the Landau-Lifshitz equa tion at low temperatures and the Bloch equation at high temperatures. It is shown that for the classical model where spin-bath interactions are described by stochastic Langevin fields and spin-spin interactions are treated within the mean-field approximation (MFA), such a ''Landa u-Lifshitz-Bloch'' (LLB) equation can be derived exactly from the Fokk er-Planck equation, if the external conditions change slowly enough. F or weakly anisotropic ferromagnets within the MFA the LLB equation can be written in a macroscopic form based on the free-energy functional interpolating between the Landau free energy near T-C and the ''microm agnetic'' free energy, which neglects changes of the magnetization mag nitude /M/, at low temperatures.